Accelerating Training of Recursive Reasoning Models with Curriculum Guided Adaptive Recursion

TL;DR

CGAR tackles the high computational cost of training recursive reasoning models by introducing a curriculum over architectural depth (Progressive Depth Curriculum) and a gradient-aware loss weighting (Hierarchical Supervision Weighting). On Sudoku-Extreme, this approach yields a 1.71× training speedup with minimal accuracy loss, and ablations show PDC as the dominant contributor (2.26× speedup) while HSW provides additional variance reduction (~1.61×). The method reduces training FLOPs by 41.4% and improves inference efficiency with 100% halting accuracy and fewer reasoning steps, making recursive reasoning models more accessible on standard hardware. The work highlights a rare Pareto improvement for architectural curricula and suggests broad potential for efficiency gains in neurosymbolic AI and related reasoning tasks, while outlining avenues for cross-task validation and automation of curriculum design.

Abstract

Recursive reasoning models achieve remarkable performance on complex reasoning tasks through iterative refinement, enabling tiny networks to match large language models thousands of times their size. However, training remains computationally expensive, prior work reporting approximately 36 GPU-hours per dataset, limiting broader adoption and research. We propose CGAR, a novel training methodology that applies curriculum learning to architectural depth rather than traditional data ordering. CGAR introduces two synergistic components: Progressive Depth Curriculum dynamically adjusts recursion depth from shallow to deep configurations during training, preventing early overfitting while reducing computational cost, and Hierarchical Supervision Weighting applies exponentially decaying importance to supervision steps, aligning loss weighting with observed gradient magnitude decay. On Sudoku-Extreme with 423,168 test puzzles, CGAR achieves 1.71x training speedup (10.93 to 6.38 hours, 42% cost reduction) with only 0.63% accuracy drop (86.65% to 86.02%). Systematic ablations reveal Progressive Depth Curriculum alone achieves 2.26x speedup with 85.47% accuracy, demonstrating a rare Pareto improvement where architectural curriculum simultaneously enhances training efficiency and solution quality. CGAR-trained models exhibit superior inference efficiency with 100% halting accuracy and 11% fewer reasoning steps. Our work demonstrates that principled curriculum on architectural depth enables efficient training of recursive reasoning models on modest hardware. Code and models: https://github.com/Kaleemullahqasim/CGAR and https://huggingface.co/Kaleemullah/trm-cgar-sudoku

Figures (4)

• Figure 1: Illustration of CGAR architecture follows TRM with recursive transformer blocks. CGAR introduces two key modifications: Progressive Depth Curriculum (PDC) adjusts recursion depth $(n,T)$ across training phases, and Hierarchical Supervision Weighting (HSW) applies exponential decay $w_t = \lambda^{t-1}$ to supervision losses.
• Figure 2: CGAR Training with Progressive Curriculum and Hierarchical Weighting
• Figure 3: Example of CGAR solving a Sudoku-Extreme puzzle in 2 reasoning steps. The model starts with the initial puzzle, performs one intermediate refinement step, and produces the complete solution. This demonstrates efficient adaptive computation where the model learns to halt after sufficient reasoning.
• Figure 4: CGAR generalization analysis across checkpoints. Consistent $\sim$1.3% train-test gap indicates excellent generalization without overfitting.